Can you solve a Disk, Washer, Shell method problem without drawing a graph?

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Discussion Overview

The discussion revolves around whether it is possible to solve problems involving the Disk, Washer, and Shell methods without creating a graph. Participants explore the necessity and utility of graphical representations in setting up integrals correctly.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants question if it is feasible to solve these problems without a graph, suggesting that a graph serves as a visual aid to ensure the integrals are set up correctly.
  • Others express concern that not drawing a graph might lead to mistakes, such as incorrectly identifying which equations to subtract.
  • One participant argues against the idea of avoiding graphing due to potential inaccuracies, suggesting that the solution lies in improving one's graphing skills rather than skipping the step entirely.

Areas of Agreement / Disagreement

Participants do not reach a consensus; there are competing views on the necessity of drawing graphs for solving these problems, with some advocating for their importance and others questioning their necessity.

Contextual Notes

Some participants express personal experiences with graphing inaccuracies affecting their problem-solving, highlighting the subjective nature of the graphing process and its impact on understanding the problem.

Vividly
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Solving the problem
Is there a way to solve a Disk,Washer,Shell method problem without actually creating a graph?
 
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Isn't the graph just a visual aid to insure you've setup the integrals correctly?

I'm sure it will give you extra points should you get the wrong answer but have visualized it correctly meaning you should do it for that additional reason alone.
 
Vividly said:
Is there a way to solve a Disk,Washer,Shell method problem without actually creating a graph?
Why would you want to not draw a graph?
 
Mark44 said:
Why would you want to not draw a graph?
Because sometimes I may not draw the graph perfectly and may miss which equation is suppose to be subtracted from the other. I had this happen before.
 
Vividly said:
Because sometimes I may not draw the graph perfectly and may miss which equation is suppose to be subtracted from the other. I had this happen before.
Not wanting to sketch a graph because you might not do it perfectly is a terrible reason. If you have a problem drawing the graph correctly, the solution is not to skip this important step -- it's to learn how to make the graph good enough to be useful.

What you're saying sounds to me like a situation where somebody needs to get a bunch of items at the store, but doesn't want to write down the list of items because of poor handwriting ability.
 
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